Basically, this is how it looks: if one wave a non-sinusoidal wave, it is already composed of several sinusoidal waves, most typically -- infinite number of those. If the signal is non-periodic, you have not a countable infinite number of components, but continuum of those. In brief, the idea is that each the set of sinusoidal wave makes an infinite-dimensional space formed by the infinite-dimensional basic of orthogonal vectors, each representing a sinusoidal wave. They are orthogonal in the following sense: integral of the product of any two of them from minus to plus infinity is zero. You can decompose any signal into its sinusoidal component, which is a main task of
spectral analysis.
Now, here is the problem: even though you can decompose the summary signal of your ECG signals into a set of sinusoidal components,
you cannot separate original ECG signals from each other. This is
because they are not orthogonal: only their sinusoidal components are. Roughly speaking: even though you could perform spectral analysis of each ECG signal, and even though you can do the same with the sum of several ECG signal with the same components, there is no a way to determine which of them "belonged" to which ECG signal.
Interestingly, in the space of frequencies, separation of the spectrum curves from different sources is possible, to certain extent, if there is some essential a priory information on the expected shape. Such mathematical technique is used in optical spectroscopy.
In the case of ECG, where the original measured signal is dependency on time (not a spectrum), the task looks hopeless to me. I'm just curious: how happens that several ECG signals was entangled together in first place? I saw such records many times; usually individual signals from different sensors are recorded. Something is wrong with your task…
Please see:
http://en.wikipedia.org/wiki/Functional_analysis[
^],
http://en.wikipedia.org/wiki/Spectral_Analysis[
^],
http://en.wikipedia.org/wiki/Fourier_space[
^],
http://en.wikipedia.org/wiki/Fourier_transform[
^],
http://en.wikipedia.org/wiki/FFT[
^].
—SA